Partnership - 05

Explanation:-

∵ Loss will be divided according to their investment ratio =

A	:	B
3000	:	2400
5	:	4

$$\eqalign{ & {\text{Loss of B}} = \frac{4}{{\left( {5 + 4} \right)}} \times 720 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 320}} \cr}$$

Explanation:-

$$\eqalign{ & {\text{Investment of A for 8 months}} \cr & = {\text{Rs}}{\text{.15400}} \cr & {\text{Investment of B for 6 months}} \cr & = {\text{Rs}}{\text{.18200}} \cr & {\text{Investment of C for 8 months}} \cr & = {\text{Rs}}{\text{.12600}} \cr & {\text{Ratio of the share of A, B and C}} \cr & = 15400 \times 8:18200 \times 6:12600 \times 8 \cr & = 154 \times 8:182 \times 6:126 \times 8 \cr & = 44:39:36 \cr & {\text{Sum of the terms of ratio}} \cr & = 44 + 39 + 36 \cr & = 119 \cr & \therefore {\text{ Share of C}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{36}}{{119}} \times 28790} \right) \cr & = {\text{Rs}}{\text{.8710}} \approx {\text{Rs}}{\text{.8712}} \cr}$$

Explanation:-

Let their investments be Rs. 3x for p months
Rs. 4x for q months and Rs. 6x for r months respectively
Then,
$$\eqalign{ & 3xp:4xq:6xr = 1:1:1 \cr & {\text{So,}}3p = 4q \cr & \Leftrightarrow q = \frac{{3p}}{4} \cr & {\text{And, }}4q = 6r \cr & \Leftrightarrow r = \frac{{2q}}{3} = \left( {\frac{2}{3} \times \frac{3}{4}p} \right) = \frac{p}{2} \cr & \therefore p:q:r \cr & = p:\frac{{3p}}{4}:\frac{p}{2} \cr & = 4:3:2 \cr}$$

Explanation:-

	A	:	B	:	C
Ratio of Profit →	2	:	3	:	7

$$\eqalign{ & {\text{Average gain}} = \frac{{2 + 3 + 7}}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 4{\text{ units}} \cr & {\text{According to the question,}} \cr & {\text{4 units}} = {\text{Rs}}{\text{. 8000}} \cr & {\text{1 unit}} = {\text{Rs}}{\text{. 2000}} \cr & {\text{3 units}} = 3 \times 2000 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 6000}} \cr & \therefore {\text{Share of B}} = {\text{Rs}}{\text{. 6000}} \cr}$$

Explanation:-

Let C subscribes the business = Rs. x
A : B : C
Capital → (x + 12000) : (x + 5000) : x
Note: Profit would be divide in the ratio of their capitals
According to the question,
$$\eqalign{ & \Rightarrow \left( {x + 12000} \right) + \left( {x + 5000} \right) + x = 47000 \cr & \Rightarrow 3x + 17000 = 47000 \cr & \Rightarrow 3x = 30000 \cr & \Rightarrow x = 10000 \cr & {\text{ A }}:{\text{ B }}:{\text{ C}} \cr & {\text{Capital}} \to 22000:15000:10000 \cr & {\text{Profit}} \to {\text{ }}22{\text{ }}:{\text{ }}15{\text{ }}:{\text{ }}10 \cr & \left( {22 + 15 + 10} \right){\text{ units}} = {\text{4700}} \cr & {\text{1 unit}} = \frac{{4700}}{{47}} = 100 \cr & {\text{Share of C}} = 10{\text{ units}} = 10 \times 100 = {\text{Rs}}.1000 \cr & \cr}$$

Explanation:-

$$\eqalign{ & {\text{Shankar}}:{\text{Aniket}} \cr & = \left( {6000 \times 12} \right):\left( {35000 \times 8} \right) \cr & = 720000:280000 \cr & = 18:7 \cr}$$

Explanation:-

$$\eqalign{ & A:B \cr & = \left[ {4x \times 3 + \left( {4x - \frac{1}{4} \times 4x} \right) \times 7} \right]:\left[ {5x \times 3 + \left( {5x - \frac{1}{5} \times 5x} \right) \times 7} \right] \cr & = \left( {12x + 21x} \right):\left( {15x + 28x} \right) \cr & = 33x:43x \cr & = 33:43 \cr & \therefore {\text{A's}}\,{\text{share}} = Rs.\,\left( {760 \times \frac{{33}}{{76}}} \right) \cr & = Rs.\,330 \cr}$$

Explanation:-

$$\eqalign{ & {\text{Let}}\,{\text{B's}}\,{\text{capital}}\,{\text{be}}\,Rs.\,x \cr & {\text{Then}},\,\left( {\frac{{3500 \times 12}}{{7x}} = \frac{2}{3}} \right) \cr & \Rightarrow 14x = 126000 \cr & \Rightarrow x = 9000 \cr}$$

Explanation:-

$$\eqalign{ & {\text{Let their investments be}}\, \cr & Rs.\,x\,{\text{for}}\,{\text{14}}\,{\text{months}},\, \cr & Rs.\,y\,{\text{for}}\,{\text{8}}\,{\text{months}}\,{\text{and}}\, \cr & Rs.\,z\,{\text{for}}\,{\text{7}}\,{\text{months}}\,{\text{respectively}}. \cr & {\text{Then}},\,14x:8y:7z = 5:7:8 \cr & {\text{Now}},\frac{{14x}}{{8y}} = \frac{5}{7} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,98x = 40y \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,y = \frac{{49}}{{20}}x \cr & {\text{And}},\frac{{14x}}{{7z}} = \frac{5}{8} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,112x = 35z \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,z = \frac{{112}}{{32}}x = \frac{{16}}{5}x \cr & \therefore x:y:z \cr & = x:\frac{{49}}{{20}}x:\frac{{16}}{5}x \cr & = 20:49:64 \cr}$$

Explanation:-

$$\eqalign{ & {\text{Ratio}}\,{\text{of}}\,{\text{initial}}\,{\text{investments}} \cr & = \left( {\frac{7}{2}:\frac{4}{3}:\frac{6}{5}} \right) = 105:40:36 \cr & {\text{Let}}\,{\text{the}}\,{\text{initial}}\,{\text{investments}}\,{\text{be}} \cr & 105x,\,40x\,{\text{and}}\,36x \cr & \left( {105x \times 4 + \frac{{150}}{{100}} \times 105x \times 8} \right):\left( {40x \times 12} \right):\left( {36x \times 12} \right) \cr & = 1680x:480x:432x = 35:10:9 \cr & {\text{Hence,}}\,{\text{B's}}\,{\text{share}} \cr & = Rs.\,\left( {21600 \times \frac{{10}}{{54}}} \right) \cr & = Rs.\,4000 \cr}$$